Optimal Design of Filters for Multirate Systems

帕克斯：这项研究的目的是开发最优多速率数字滤波器的设计程序。用于最优性的准则是从表示过滤器的线性算子的范数中推导出来的。当应用于线性时不变滤波器的设计时，这种最佳性度量降低到通常的切比雪夫频域误差标准。对于多速率系统，这种方法给出了一种新的最优滤波准则。这提供了一种定量的分析设计程序，比通常使用的直观设计方法产生更好的过滤器。用于开发适当误差函数的方法使用来自周期时变线性系统的奇异值分解和分析的技术。开发高效的设计算法是基于半无限规划和类Remez多重交换方法。这项研究有望为多速率滤波器的性能设定极限，并提供改进的滤波器。目前的设计可以与最好的设计进行比较，以确定可能的改进。

Parks The objective of this research is to develop procedures for the design of optimum multirate digital filters. The criterion used for optimality is derived from the norm of a linear operator that represents the filter. When applied to the design of linear, time-invariant filters this measure of optimality reduces to the usual Chebyshev frequency domain error criterion. For multirate-systems, this approach leads to a new criterion for filter optimality. This provides a quantitative, analytic design procedure that yields better filters than intuitive design methods that are in common use. The methods for the development of appropriate error functions use techniques from singular value decomposition and analysis of periodically time-varying linear systems. The development of efficient design algorithms is based on semi-infinite programming and Remez-like multiple exchange methods. This research is expected to establish limits for performance of multirate filters as well as to provide improved filters. Present designs can be compared with the best attainable to determine possible improvements.